A method for stability analysis of high-speed boundary layer flow considering aircraft wall radiation

Abstract

The application discloses a high-speed boundary layer flow stability analysis method considering aircraft wall radiation, and comprises the following steps: S1, a basic flow is obtained by compiling a Navier-stokes equation solver for numerical simulation of hypersonic aircraft flow; S2, the thermal physical property parameters of the gas are calculated by adopting the calorimetric perfect gas assumption, and for the case that the Mach number is 4.5-8, the high-temperature real gas effect is not considered, that is, the specific heat is still a constant specific heat; S3, the adiabatic energy balance condition is adopted, the aircraft wall radiation is considered when the aircraft wall boundary condition is set, and the gas radiation is ignored, and at this time, the temperature corresponding to the aircraft wall is called the radiation equilibrium temperature; S4, the linear stability theory (LST) is adopted to perform flow stability analysis on the basic flow considering the aircraft wall radiation and ignoring the gas radiation, and neutral curves and maximum growth rate results are obtained.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, and in particular to a method for analyzing the stability of high-speed boundary layer flows considering radiation from the aircraft wall. Background Technology

[0002] Past studies on the stability of supersonic boundary layer flows have primarily employed adiabatic or isothermal vehicle wall conditions, neglecting the radiative heat transfer at the vehicle wall surface when high-speed airflow causes significant temperature fluctuations. While these conditions hold true in laboratory settings—for example, isothermal conditions are suitable for calculating initial cold wall heat flux, and adiabatic conditions are suitable for long-duration experiments—these conditions are unsuitable for actual long-duration hypersonic flights. In such cases, the wall temperature is at radiation equilibrium, significantly different from the adiabatic wall temperature without considering radiation. Since the vehicle wall temperature directly affects the basic flow profile, the boundary layer flow stability characteristics change considerably. Therefore, it is necessary to establish theories and methods for flow stability analysis that consider high-temperature vehicle wall radiation to obtain results consistent with real-world conditions. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art and solve the problem that the boundary layer flow of hypersonic vehicles in actual flight does not consider the thermal insulation of the vehicle wall radiation in the flow stability analysis. The invention proposes to consider the heat transfer of vehicle wall radiation and couple it with airflow, providing a more accurate basic flow profile and flow stability analysis method.

[0004] The objective of this invention is achieved through the following technical solution:

[0005] A method for analyzing the stability of high-speed boundary layer flows considering radiation from the aircraft wall includes:

[0006] S1. Write a solver for the Navier-Stokes equations required for numerical simulation of flow around a hypersonic vehicle to solve the basic flow field;

[0007] S2. The airflow around the aircraft satisfies the properties of a calorimetric perfect gas, which is suitable for Mach numbers of 4.5-8, that is, the specific heat is still a constant specific heat;

[0008] S3. The spacecraft wall satisfies energy balance. When setting the adiabatic boundary conditions of the spacecraft wall, the radiation of the spacecraft wall is considered and the gas radiation is ignored. The temperature corresponding to the spacecraft wall at this time is called the radiation balance temperature.

[0009] S4. The linear stability theory (LST) is used to perform flow stability analysis on the basic flow that considers the radiation from the aircraft wall and neglects gas radiation, and the neutral curve and maximum growth rate results are obtained.

[0010] Furthermore, in step S3: establish the energy conservation equation for the spacecraft wall, and input the total heat flux q into the spacecraft wall. total Represented as:

[0011] q total =q gw +q rad,e -q Rad,w

[0012] Where: q gw q represents the heat flow from the gas to the spacecraft walls via thermal conduction. rad,e q represents the radiative heat flux transferred from the surrounding environment to the aircraft walls. rad,w The radiative heat flow transferred outward from the aircraft wall;

[0013] For an adiabatic wall, the total heat flux into the spacecraft wall is 0, therefore:

[0014] 0 = q gw +q rad,e -q Rad,w

[0015] According to Fourier's law and Stefan-Boltzmann's law of heat conduction, the specific expressions for the three terms on the right side of the equation are as follows:

[0016]

[0017] Where: κ is the thermal conductivity of air, n is the normal vector of the aircraft wall, ε is the emissivity of the aircraft wall material (a fixed value is taken under the gray body assumption), and the emissivity of the surrounding environment is taken to be the same as that of the aircraft wall material, σ = 5.67 × 10 -8 (W / (m 2 ·K 4 )) represents the Stefan-Boltzmann constant, the subscript e indicates the environmental quantity, the subscript w indicates the spacecraft wall quantity; T is the dimensionless temperature.

[0018] Furthermore, in step S4:

[0019] For hypersonic boundary layer flow, the perturbation within the boundary layer can be written in the following form:

[0020]

[0021] in Let ω be the shape function of the disturbance, α, β, and ω be the flow wavenumber, spanwise wavenumber, and frequency, respectively, and cc represent the conjugate complex number. If we consider the spatial pattern, i.e., the disturbance grows along space, then the frequency ω is a real number, and α and β are complex numbers, i.e., α = α r +iα i,β=β r +iβ i At this point, a real function factor will appear in the perturbation. and If α i <0 or β i If < 0, the disturbance will grow exponentially along the positive x or z direction, therefore the negative of the imaginary parts of α and β, -α i -β i Let β and α represent the spatial growth rates in the flow direction and spanwise, respectively. For a two-dimensional flow field, β = 0, meaning that only the spatial growth rate in the flow direction, -α, exists. i ;

[0022] Substituting the above perturbation solution into the stability OS equation, the perturbation at the spacecraft wall and normal infinity is 0, thus realizing the stability analysis calculation.

[0023] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0024] (1) The theory and analysis method proposed in this invention are more in line with the actual long-endurance flight flow conditions of hypersonic aircraft, laying the foundation for accurate prediction of transition, improving the accuracy of aircraft wall temperature calculation, and thus improving the accuracy of aerodynamic and aerothermal calculation results, providing a design basis for the aerodynamic layout and thermal protection design of actual aircraft.

[0025] (2) The method is easy to implement. By considering the radiation characteristics of the aircraft wall through boundary conditions, the computational load is not increased compared to the previous adiabatic boundary conditions. Different radiation characteristics of aircraft wall materials can be considered by changing the radiation coefficient of the aircraft wall.

[0026] (3) It provides a research approach for further calculations of complex flows such as gas radiation that are necessary to consider at higher temperatures. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the energy balance relationship of the aircraft wall.

[0028] Figure 2 This is a schematic diagram of hypersonic flat plate flow.

[0029] Figure 3 The variation of the aircraft wall temperature with or without radiation at Mach number M=6 is given by position along the flow direction, where the x-axis represents the position x along the flow direction of the aircraft wall, and the y-axis represents the dimensionless aircraft wall temperature T of the incoming flow temperature. w .

[0030] Figure 4 is a comparative diagram of the basic flow velocity, temperature, and their first and second derivative profiles on the surface of an aircraft with and without radiation at Mach number M=6. The horizontal axis represents the position y along the normal direction of the aircraft surface. Figure 4aDimensionless flow velocity profile; Figure 4b Dimensionless temperature profile; Figure 4c Dimensionless flow velocity first derivative profile; Figure 4d Dimensionless temperature first derivative profile; Figure 4e Second derivative profile of flow velocity; Figure 4f Dimensionless temperature second derivative profile.

[0031] Figure 5a A comparison of neutral curves with and without radiation on the surface of an aircraft with Mach number M=6, where the horizontal axis represents the position x along the flow direction on the surface of the aircraft and the vertical axis represents the frequency ω of the unstable wave; Figure 5b This is a comparison chart showing the maximum growth rate with and without radiation on the aircraft wall. The horizontal axis represents the position x along the flow direction on the aircraft wall, and the vertical axis represents the maximum growth rate - α. i,max .

[0032] Figure 6a A comparison of the amplitude evolution results calculated by two methods (LST and DNS) for the surface of an aircraft with Mach number M=6 without considering radiation; Figure 6b Comparison of amplitude evolution results for M=6 aircraft wall calculation using two methods (LST, DNS), where the horizontal axis represents the position x along the flow direction of the aircraft wall and the vertical axis represents the amplitude A.

[0033] Figure 7a , Figure 7b The figures represent the variation of the aircraft wall temperature with and without radiation at Mach numbers M=4.5 and 8, respectively. The horizontal axis represents the position x along the flow direction of the aircraft wall, and the vertical axis represents the dimensionless aircraft wall temperature T, derived from the incoming flow temperature. w .

[0034] Figure 8a , Figure 8b A comparison of neutral curves and maximum growth rate for aircraft walls with and without radiation at Mach number M=4.5; Figure 8c , Figure 8d This is a comparison of neutral curves and maximum growth rate curves with and without radiation on the walls of a Mach 8 spacecraft. The horizontal axis represents the position x along the flow direction on the spacecraft wall, and the vertical axes represent the frequency ω of the unstable wave and the maximum growth rate -α, respectively. i,max . Detailed Implementation

[0035] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0036] This embodiment provides a method for analyzing the stability of high-speed boundary layer flows considering radiation from the aircraft wall, as detailed below:

[0037] S1. Develop a solver for the Navier-Stokes equations required for numerical simulation of flow around a hypersonic vehicle to solve the basic flow field. In this embodiment, the dimensionless conserved form of the Navier-Stokes equations for two-dimensional compressible flow of a perfectly gaseous calorimetric gas in Cartesian coordinates is:

[0038]

[0039] Where: x and y correspond to the flow direction and normal direction coordinates, respectively; t is time; U = [ρ, ρu, ρv, ρe] T For conserved fluxes, E and F are convective fluxes; E v F v This refers to viscous fluxes. The specific expressions for each flux are as follows:

[0040]

[0041] Where: ρ is the dimensionless density, u and v are the dimensionless velocities in the x and y directions respectively, p is the dimensionless pressure, and the dimensionless characteristic scales are ρ and ρ. ∞ U ∞ and The subscript "∞" indicates the incoming flow parameter. The dimensionless scale for length is L. ref . Let γ be the total energy per unit mass, q be the heat flux vector simulated according to Fourier's law, and γ be the specific heat ratio. E and F are the convection fluxes in the x and y directions, respectively. v and F v τ represents the viscous flux in the x and y directions, respectively. ij Let be the shear stress tensor. The viscous stress components and heat flux components are as follows:

[0042]

[0043]

[0044] In the formula, μ is the dynamic viscosity coefficient, calculated using Sutherland's formula, Pr = 0.72 is the Prandtl number, T is the dimensionless temperature, and the dimensionless characteristic temperature is T0. ∞ , For the incoming Mach number, Re = ρ ∞ U ∞ L ref / μ ∞ It is the Reynolds number.

[0045] Gases satisfy the equation of state for a perfect gas:

[0046]

[0047] S2. The calculation of the thermal properties of the gas adopts the calorimetric assumption of a perfect gas. For Mach numbers of 4.5-8, the effect of high-temperature real gas does not need to be considered, that is, the specific heat is still a constant specific heat, etc.

[0048] S3. Using adiabatic energy balance conditions, when setting the boundary conditions of the aircraft wall, the radiation of the aircraft wall is considered, while gas radiation is ignored. At this time, the temperature of the aircraft wall is called the radiation equilibrium temperature. The main components of air are nitrogen and oxygen, both of which are symmetrical diatomic gases. When the thickness is not very large and the temperature is below several thousand K, the emissivity and absorptivity of the gas are very small and can be ignored. It can be approximately considered that its emissivity and absorptivity are both zero, that is, the gas does not participate in radiation.

[0049] S4. The boundary conditions of the aircraft wall adopt adiabatic energy balance, and the corresponding temperature is called the radiation equilibrium temperature. The energy conservation equation for the aircraft wall is established (see...). Figure 1 The total heat flux q transferred to the spacecraft wall total It can be represented as:

[0050] q total =q gw +q rad,e -q Rad,w ,

[0051] Where: q gw q represents the heat flow from the gas on the spacecraft wall to the spacecraft. rad,e q represents the radiative heat flux transferred from the surrounding environment (other surfaces of the aircraft, etc.) to the aircraft walls. rad,w This refers to the radiative heat flow that is transferred outward from the surface of the aircraft.

[0052] When the total heat flux entering the spacecraft wall is 0, we have:

[0053] 0 = q gw +q rad,e -q Rad,w

[0054] According to Fourier's law and Stefan-Boltzmann's law of heat conduction, the specific expressions for the three terms on the right side of the equation are as follows:

[0055]

[0056] Where: κ is the thermal conductivity of air, n is the normal vector of the aircraft wall, ε is the emissivity of the aircraft wall material (a fixed value is taken under the gray body assumption), and the emissivity of the surrounding environment is taken to be the same as that of the aircraft wall material, σ = 5.67 × 10 -8 (W / (m 2 ·K 4)) is the Stefan-Boltzmann constant, the subscript e indicates the environmental quantity, and the subscript w indicates the aircraft wall quantity.

[0057] S5. Linear Stability Theory (LST) is used to analyze the flow stability of the basic flow considering radiation from the aircraft wall, obtaining results such as the neutral curve and maximum growth rate. For hypersonic boundary layer flow on a flat plate, the mean flow assumption of LST is quasi-parallel. The disturbance can be written in the following form:

[0058]

[0059] in Let ω be the shape function of the perturbation, α, β, and ω be the flow wavenumber, spanwise wavenumber, and frequency, respectively, and cc represent the conjugate complex number. If we consider a spatial pattern, i.e., the perturbation grows along space, then the frequency ω is a real number, and α and β are complex numbers, i.e., α = α r +iα i ,β=β r +iβ i At this point, a real function factor will appear in the perturbation. and It is easy to see if α i <0 or β i If < 0, the disturbance will grow exponentially along the positive x or z direction, therefore the negative of the imaginary parts of α and β, -α i -β i Let β and α represent the spatial growth rates in the flow direction and spanwise, respectively. For a two-dimensional flow field, β = 0, meaning that only the spatial growth rate in the flow direction, -α, exists. i .

[0060] By substituting the above perturbation solution into the stability OS equation, and assuming that the perturbation at the spacecraft wall and normal infinity is 0, stability analysis calculations can be performed.

[0061] Specifically, the following describes the hypersonic flat plate boundary layer (e.g., Mach 6) descending from a flight altitude of 30 kilometers. Figure 2 The figure shown is the research object, and the implementation of this analysis method will be further explained with reference to the accompanying figure.

[0062] Ambient temperature T at an altitude of 30km ∞ =226.5K, Mach number 6, the gas satisfies the properties of a calorimetric perfect gas.

[0063] The fundamental flow field quantities ρ, u, v, T, P are dimensionless using free flow parameters, i.e., temperature T. e Density ρ e Speed ​​U e Feature length L ref=0.001m. The calculation of the basic flow is a two-dimensional problem, in which the convection term adopts the fifth-order WENO scheme, the viscous term adopts the sixth-order central difference scheme, and the time progression adopts the third-order Runge-Kutta scheme.

[0064] The aircraft wall employs adiabatic boundary conditions, comparing both non-radiative and radiative scenarios. The common surface emissivity (ε) of heat-resistant materials for hypersonic aircraft walls is typically taken as 0.85. When dealing with the adiabatic boundary conditions under radiative conditions, the temperature of the aircraft wall in the flow field is determined through direct numerical simulation by solving a univariate quartic equation. The temperature at the grid points on the aircraft wall is obtained using Newton-Raphson iteration.

[0065] The basic flow field was obtained through direct numerical simulation. To avoid the influence of the leading-edge oblique shock wave, flow stability analysis was performed in the region of x = 200–1000, considering the effects of radiation-free aircraft wall temperature, for example... Figure 3 As shown, from Figure 3 It is evident that the temperature of the non-radiative adiabatic wall remains almost constant along the flow path, while the radiation equilibrium temperature of the aircraft wall decreases along the flow direction.

[0066] Figures 4a to 4f A comparison of cross-sections of the flow velocity u, temperature T, and normal first and second derivatives at position x = 80° with and without radiation at Ma = 6 is given. Figure 4a Flow velocity; Figure 4b temperature; Figure 4c First derivative of the flow velocity; Figure 4d First derivative of temperature; Figure 4e Second derivative of flow velocity; Figure 4f The second derivative of temperature. As can be seen from Figure 4, radiation from the aircraft wall causes changes in both the flow velocity and temperature profile of the basic flow field.

[0067] After obtaining the basic flow, flow stability analysis was performed using Linear Stability Theory (LST). The neutral curve and the maximum growth rate along each flow direction profile are shown below. Figure 5a , Figure 5b Given. Among them, Figure 5a The neutral curve for the region x = 0 to 1000 is given. From... Figure 5a It is evident that, at the same flow direction, due to differences in the aircraft wall conditions, the unstable frequency range corresponding to the neutral curve also differs, with the radiating unstable region generally shifting towards higher frequencies; from Figure 5b It can be seen that the maximum growth rate of each profile gradually decreases along the flow direction, but for the same flow direction location, the maximum growth rate of the radiative profile is always higher than that of the non-radiative profile.

[0068] For both cases where aircraft wall radiation is not considered and is considered, the basic flow x = 300 is taken as the computational domain inlet, and a TS disturbance wave is introduced, with the frequency taken as the value of the corresponding maximum growth rate. The initial disturbance amplitude is A0 = 1 × 10⁻⁶. -6 The amplitude evolution curves with and without radiation were calculated using Direct Numerical Simulation (DNS) and compared with the results calculated using Linear Stability Theory (LST). The amplitude evolution results calculated using these two methods are shown below. Figure 6a , Figure 6b As shown, Figure 6a The amplitude evolution is given without considering radiation from the aircraft wall. Figure 6b The amplitude evolution considering the radiation from the aircraft wall is presented. It is evident that the amplitude evolution results are consistent, demonstrating the reliability of both direct numerical simulation and linear stability analysis methods.

[0069] Furthermore, based on the above implementation process, a comparison of the variation of the aircraft wall temperature along the flow direction with and without radiation is presented for two operating conditions with incoming Mach numbers of 4.5 and 8. The results are as follows: Figure 7a and Figure 7b As shown, the radiation equilibrium temperature of the aircraft wall is lower than the temperature of the non-radiative adiabatic wall, and the difference between the two increases with the increase of Mach number.

[0070] Figure 8a , Figure 8b The neutral curves for radiation on the walls of a Mach 4.5 aircraft and the variation of the maximum growth rate along the flow direction are presented. Figure 8c , Figure 8d The neutral curves for the Mach 8 spacecraft wall with and without radiation, and the variation of the maximum growth rate along the flow direction, are presented. It can be seen that when radiation is considered, the unstable region shifts towards higher frequencies, and the maximum growth rate increases.

[0071] This invention is not limited to the embodiments described above. The above description of specific embodiments is intended to illustrate and explain the technical solutions of this invention. The specific embodiments described above are merely illustrative and not restrictive. Without departing from the spirit and scope of the claims, those skilled in the art can make many specific modifications based on the teachings of this invention, and these modifications all fall within the scope of protection of this invention.

Claims

1. A method for analyzing the stability of high-speed boundary layer flows considering radiation from the aircraft wall, characterized in that, include: S1. Develop a solver for the Navier-Stokes equations required for numerical simulation of flow around a hypersonic vehicle to solve the basic flow field; S2. The airflow around the aircraft satisfies the properties of a perfect gas with calorimetric heat, which is suitable for Mach numbers of 4.5-8, that is, the specific heat is still a constant specific heat; S3. Set the adiabatic boundary conditions for the aircraft wall, consider radiation from the aircraft wall, neglect gas radiation, establish the energy conservation equation for the aircraft wall, and input the total heat flux into the aircraft wall. Represented as: ； in: This refers to the heat flow from the gas being transferred to the spacecraft walls through heat conduction. This refers to the radiative heat flow transferred from the surrounding environment to the aircraft walls. The radiative heat flow transferred outward from the aircraft wall; For an adiabatic wall, the total heat flux into the spacecraft wall is 0, therefore: ； According to Fourier's law and Stefan-Boltzmann's law of heat conduction, the specific expression is as follows: ； in: The thermal conductivity of air. Let be the normal vector of the aircraft wall. The emissivity of the aircraft wall material is determined by taking a fixed value under the gray body assumption, while the emissivity of the surrounding environment is taken as the same as that of the aircraft wall material. This is the Stefan-Boltzmann constant. Indicates ambient temperature. Indicates the surface temperature of the aircraft wall; The surface temperature of the aircraft was obtained by Newton's iteration method. That is, the radiation equilibrium temperature; S4. The linear stability theory (LST) was used to perform flow stability analysis on the basic flow that takes into account the radiation from the aircraft wall and neglects gas radiation, and the neutral curve and the maximum growth rate results were obtained.

2. The method for analyzing the stability of high-speed boundary layer flow considering aircraft wall radiation according to claim 1, characterized in that, In step S4: For hypersonic boundary layer flow, the perturbation within the boundary layer can be written in the following form: in Let be the shape function of the perturbation. and These are the flow wavenumber, spanwise wavenumber, and frequency, respectively. Represents the conjugate complex number; if spatial patterns are considered, i.e., the disturbance grows along space, then the frequency... For real numbers, and It is a complex number, that is At this point, a real function factor will appear in the perturbation. and ;like or The disturbance will then proceed along positive or Positive exponential growth, therefore and The opposite of the imaginary part Let these represent the spatial growth rates in the flow direction and spanwise direction, respectively. For a two-dimensional flow field, we have: That is, only the spatial growth rate of the flow exists. ; Substituting the above perturbation solution into the stability OS equation, the perturbation at the spacecraft wall and normal infinity is 0, thus realizing the stability analysis calculation.

Images